The invention relates to a coupling device (10), in particular for industrial applications, for torque-transmitting connection of two shaft segments, comprising a first coupling part (12) for coupling with a first shaft segment and a second coupling part (16) for coupling with a second shaft segment, wherein the first coupling part (12) has a plurality of coupling projections (26) arranged in regular angular intervals around a centre axis (A) of the first coupling part, wherein the second coupling part (16) has a corresponding plurality of coupling projections (24) arranged in regular angular intervals around a centre axis of the second coupling part (16), at least two coupling projections (24, 26) of the first and second coupling part (12, 16) adjacent to each other each having a power-transmitting connection by means of an elastic connection arrangement (42), wherein the elastic connection arrangement (42) has two connecting links (44, 46) angled relative to one another, which extend between the adjacent coupling projections (24, 26), wherein the connecting links (44, 46) have a power-transmitting coupling to regions facing each other having at least one tension strand portion (54) substantially running in the radial direction.